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1. The flow in two dimensions of an oscillating incompressible fluid near a circular cylinder with its axis normal to the direction of oscillation, is studied theoretically and experimentally. Starting from Navier-Stoke's differential equations the method of successive approximations has been used in order to get approximative solutions, when the appropriate boundary conditions are applied. The zeroth approximation gives the modified field of oscillation near the cylinder as a function of the viscosity. The first approximation also gives a stationary flow, which is found from the solution of an ordinary linear differential equation of 4th order. 2. Experiments have been carried out in air in a Kundt's tube. The velocities in the plane normal to the axis of the cylinder have been found by photographing smoke particles in air. The experimental and theoretical results agree fairly well. Comparison with corresponding data obtained by Schlichting is also made. Some G functions, derived from Hankel functions which have been used in the theoretical solutions, have been tabulated to 6 digits. [ABSTRACT FROM AUTHOR]